

A289971


Number of permutations of [n] determined by their antidiagonal sums.


3



1, 1, 2, 4, 9, 20, 49, 114, 277, 665, 1608, 3875
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,3


LINKS

Table of n, a(n) for n=0..11.
C. Bebeacua, T. Mansour, A. Postnikov, S. Severini, On the Xrays of permutations, arXiv:math/0506334 [math.CO], 2005.
FindStat  Combinatorial Statistic Finder, The number of permutations with the same antidiagonal sums.


PROG

(Sage)
def X_ray(pi):
P = Permutation(pi).to_matrix()
n = P.nrows()
return tuple(sum(P[k1j][j] for j in range(max(0, kn), min(k, n)))
for k in range(1, 2*n))
@cached_function
def X_rays(n):
return sorted(X_ray(pi) for pi in Permutations(n))
def statistic(pi): return X_rays(pi.size()).count(X_ray(pi))
[[statistic(pi) for pi in Permutations(n)].count(1) for n in range(7)]


CROSSREFS

Cf. A019589, A002047, A290279, A290280.
Sequence in context: A123467 A124497 A286983 * A093637 A068051 A032289
Adjacent sequences: A289968 A289969 A289970 * A289972 A289973 A289974


KEYWORD

nonn,more


AUTHOR

Martin Rubey, Jul 16 2017


EXTENSIONS

a(8)a(11) from Alois P. Heinz, Jul 24 2017


STATUS

approved



